Convolutional proximal neural networks and Plug-and-Play algorithms

In this paper, we introduce convolutional proximal neural networks (cPNNs), which are by construction averaged operators. For filters with full length, propose a stochastic gradient descent algorithm on submanifold of the Stiefel manifold to train cPNNs. case limited design algorithms for minimizing functionals that approximate orthogonality constraints imposed operators penalizing least squares distance identity operator. Then, investigate how scaled cPNNs prescribed Lipschitz constant can be used denoising signals and images, where achieved quality depends constant. Finally, apply cPNN based denoisers within Plug-and-Play framework provide convergence results corresponding PnP forward-backward splitting an oracle construction.